The measurement model and structural model are two core components of structural equation modeling (SEM), a statistical technique used to test and estimate causal relationships among variables.
Measurement Model
The measurement model, also known as the outer model, specifies the relationships between observed indicators (e.g., survey questions, test scores) and their underlying latent variables (constructs that cannot be directly measured, such as customer satisfaction or intelligence). It essentially describes how well the observed indicators measure the latent variables.
Key aspects of the measurement model:
- Indicators: Observable variables used as proxies for latent variables.
- Latent Variables: Unobservable constructs that are represented by multiple indicators.
- Factor Loadings: Represent the strength and direction of the relationship between an indicator and its latent variable. Higher factor loadings indicate a stronger relationship.
- Measurement Error: Represents the degree to which an indicator fails to perfectly measure the latent variable. Every indicator has some degree of error.
- Purpose: To assess the validity and reliability of the measurement instrument. It answers the question: "Are we measuring what we think we're measuring?"
Example:
Imagine a study measuring "Customer Loyalty". The latent variable "Customer Loyalty" might be measured by indicators such as:
- "I intend to continue purchasing from this company."
- "I would recommend this company to others."
- "I consider this company to be my first choice."
The measurement model would examine how well these indicators reflect the underlying construct of "Customer Loyalty".
Structural Model
The structural model, also known as the inner model, specifies the causal relationships among the latent variables. It describes how these latent variables influence each other.
Key aspects of the structural model:
- Latent Variables: As defined in the measurement model.
- Path Coefficients: Represent the strength and direction of the relationships between latent variables. Similar to regression coefficients.
- Purpose: To test hypotheses about the relationships among latent variables. It answers the question: "How do these concepts relate to each other?"
Example:
Building on the "Customer Loyalty" example, the structural model might propose that "Customer Satisfaction" (another latent variable measured by its own indicators) predicts "Customer Loyalty". The structural model would then estimate the path coefficient representing the strength and direction of this relationship.
Relationship Between Measurement and Structural Models
In SEM, the measurement model is typically assessed before the structural model. A well-specified and validated measurement model is crucial for obtaining accurate and meaningful results in the structural model. Poorly measured constructs can lead to biased or inaccurate estimates of the relationships among them. Essentially, you want to make sure you're measuring your variables correctly before examining the relationships between them.
In summary, the measurement model validates the measures, and the structural model tests the relationships between the underlying constructs represented by those measures. Together, they provide a comprehensive framework for testing complex theories.
